Matching network



y 1939- A. ALFORD 2,165,086

MATCHING NETWORK Original Filed NOV. 19, 1936 3 Sheets-Sheet 1 INVENTORANDREW ALFORD ATTORNEY July 4, 1939. A. ALFORD MATCHING NEVTWORKOriginal Filed Ndv. 19, 1956 s Sheets-Sheet 2 lNVINTO-R ANDREW ALFORDATTORNEY July 4, 1939.

Original Filed Nov. 19, 1936 FIG".

A. ALFORD 2,165,086

MATCHING NETWORK 3 Sheets-Sheet 3 o I l l I I Lu, 1.0 Z 0 2.5 3.0 r

O .5 1.0 1.5 2.0 V T ANDREW ALFORD ATTORNEY Patented July 4, i939 U ITEDSTATES RElSSUED l-lCE Andrew Alford, New York, N. IL, i

or to Mackay .Radio and Telegraph Company, New

York, N. Y., a corporation o2 ware 13 Claims.

This invention relates to matching networks and pertains moreparticularly to networks of this character for interconnecting radioapparatus with two-wire transmission lines.

It is an object of this invention to provide an electrical network forinterconnecting a radio transmitter with a two-wire transmission line sothat it will always be insured that the two conductors of thetransmission line carry equal currents 180 out of phase.

Another object is the provision of an electrical network forinterconnecting a radio translating device with a two-wire circuitwhereby equal voltages between the two wires of the circuit and theground will'be obtained and at the same time a 180 phase relationbetween the currents in the two wires will result.

Whenever two-wire transmission lines are used to supply power to thetransmitting antennae, it is necessary to insure that the two conductorsof the transmission line carry equal currents 180 out of phase so thatthe transmission line itself will not act as an antenna and radiateenergy in all directions. When the currents in the transmission line arecharacterized as above mentioned, the line acts merely as a conductor totransfer the energy to the antenna, and undesirable radiation from thetransmission line itself is avoided.

Transmission lines can very well be balanced at the lower radiofrequency ranges by the use of known apparatus and methods withsatisfactory results, but as the frequency is increased difificultiesare encountered which have not been overcome by the teachings of theprior art. For example, with frequencies of the order of five megacyclesthe problem of supplying the line with energy in a balanced manner maybe satisfactorily solved by a number of methods employing air coretransformers.

At frequencies of the order of ten megacycles some difficulty isencountered since an ordinary air core transformer tends to pick upenergy through electrostatic coupling as well as electromagneticcoupling and therefore operates in a manner which cannot always bepredicted with certainty, with the result that the voltages at theopposite ends of the output winding are neither necessarily equal nor180 out of phase. At fifteen megacycles this condition is furtheremphasized since at this frequency electrostatic coupling is moreeflicient and exerts a greater disturbing effect. At all higherfrequencies the difficulties encountered are even greater.

It has been suggested heretofore that in order to secure the balancedesired as outlined hereinabove. the center of the secondary oi thetransformer be grounded so as to insure that the center of this coilshall be at zero potential. This condition is cult to achieve however,since the grounding connection must necessarily have some physicallength and consequently some inductance, this inductance being usuallyhigh enough so that the drop across the grounding wire at the higherfrequencies is sumcient to produce a floating potential at the center ofthe coil instead of a ed ground potential, with the result that capacitycoupling between the primary and secondary of the transformer resuitsand produces the usual undesirable efiect.

A large number of other arrangements have been suggested for obtaining abalanced condition in transmission lines, but so far as I am aware thevarious known arrangements are either extremely complicated andexpensive to construct or fail to give a balanced output at the higherfrequency ranges.

I have found that it is possible to avoid the difficulties due tocapacity coupling by the provision of an electrical network which isrelatively simple and has been found to give very satisfactory resultsin actual practice.

In accordance with my invention I provide a network of impedancesconnected across and in series with the line and between line and groundwhich serve to balance the line, causing it to have in the two wiresthereof equal currents 180 out of phase with respect to each otherwhereby undesired radiation from the line is prevented. When the line isused in conjunction with a radio receiver it similarly is free fromundesired pick-ups.

The above described and further objects and advantages of my inventionand the manner of attaining them will be more fully explained in thefollowing description taken in conjunction with the accompanyingdrawings.

In the drawings Fig. 1 illustrates a network forming one embodiment ofmy invention wherein two inductances and a condenser are used.

Figs. 2 audit illustrate other networks in accordance with my invention,utilizing two condensers and an inductance.

Fig. 4 illustrates alnothernetwork in accordance with my inventionutilizing two inductances and a condenser.

Figs. 5 and 6 are diagrams used in explainrangements 3 and 4. Figs. 11and 12 are used in further explanation of the invention.

Reierring'more particularly to the drawings, in Fig. 5 the voltagebetween the wires l-4, and 2-1, is V and the voltage between wire 2-1and the point 3 is U, the wire 2-'| being connected to ground in suchmanner that it is really at shall be equal in magnitude and opposite inground potential or it not, so that it may be assumed to be at ground orother fixed potential. Theimpedance 8-5 is A, the impedance 5-8 is B,the impedance 3-5 is ('2 and the impedance 3-4, representing thetransmission line impedance is P. Likewise the current through theimpedance A is M, and the current through the impedance P is N.

The power for supplying the currents mentioned, which may for example bederived from a vacuum tube, is assumed to be applied between terminals land 2 while the transmission line, represented by impedance P, isconnected to terminals 3 and l.

Now the condition desired to be attained is that the voltage U betweenthe point 3 and ground, and the voltage V between the point 4 andground,

phase, that is V=-U.

This result is secured when the relative values and signs of theimpedances are properly chosen as' shown by the following formulae.

(4) N(P+C)=AM s M= P+c (q) AM+ M+N =V= expanding and rearranging terms(6) becomes 1 B+A M+(B--;)1v= o (s) (B+.4)M= --B)N by substituting (5)in (8) we get then Equation (10) becomes which may be e panded as 3 (12) awn-$81 150 ac'bsasab+%as =0 Equating imaginary and real componentssep- (13) we obtain 2,186,086 utilizing-the networks of Figs. 1. 2,arately we derive two separate Equations 13 and 14 as follows: 'i+(b+a)s=ab+% 1 1 J 'i'J ar or b+;=i I Now substitutin a) for (b- -a) inEquation.

(16) c= '2b or a: 2B substituting 16 in 14 we derive (17) a=c or A=C bycomparison of 16 and 17 we get (18) a=2b or A=-2B I Thus the conditionthat V=.U regardless of the value of P may be satisfied by the twocircuits shown in Figs. 1 and 2 provided that elements of the same kind,that is the two inductances in Fig. 1 and the two capacitances in Fig. 2are equal, and when the third element is such that the impedance acrossit is equal in magnitude to onehalf of the impedance. of either one ofthe equal elements, and has an opposite sign. To assure this result thetwo inductances in Fig. 1 must be arranged in such manner as to avoid orat least keep very small, mutual reactance between 'them. And the thirdelement must be arranged in such manner that the impedance from thejunction point of the inductances in Fig. 1 to ground is equal inmagnitude to one-half of the impedance of either one of the inductances,and is of opposite sign. But this impedance need not be necessarilyconcentrated in the third element itself, that is, it is not necessarythat the condenser represented in Fig. 1 should have the exact value ofimpedance for, for instance, it is entirely possible for part of thisimpedance to be concentrated in the lead which is necessary to connectthis condenser to ground so that in actual practice, it may well be thatthe reactance of thecondenser is actually much higher than that which isrequired; the reactance oi. thelead which connects the condenser toground or for that matter partially by the inductance of the lead otherside of the condenser to the junction point 01' the inductances.

The same. of course, is true of Fig. 2, namely this time the inductanceshown as the third element is not necessarily concentrated in the coilitself but partially at least is to be found in the wire which connectsthis inductance to ground or to the junction point of the twocondensers. It is this feature of the circuit which makes it reallypractical for with this circuit it is not necessary to find a point inthe transmitter that is really at ground potential. 'Indeed all that isnecessary is that the impedance between the junction point oi thesimilar elements and ground have the required value. It has been foundexperimentally that the distributed capacity of the inductors to groundutilized in circuit I does not in practice disturb the circuit to anygreat extent. The same over all effect of such stray capacities toground is merely to alter the impedance between points yet a part of itis balanced out by which connects the p chances" 8 and 4 respectively toground, that is, in eflect merely to alter the impedance of thetransmission line as seen from terminals 3 and 4. We have already-shownabove that as long as the fundamental conditions of the circuit aresatisfied it is quite immaterial as to what the impedance of the linehappens to be for the conditions to be satisfled by the three elementsare the same irrespec= tive of the value of this impedance.

The circuits 3 and 6 may best be explained in connecttion with Fig. 6.This figure differs from Fig. 5 only in that an impedance has beenplaced between points t and a rather than between points 3 and 5. Theanalysis of this circuit is very similar to the one which has alreadybeen carried out in connection with Fig. 5.

. Assuming that V represents the voltage between conductors I-8 and 2-4;U the voltage between point 3 and ground, that is conductor 2-? and X isthe voltage between the point t and conductor 2l, then for a conditionof perfect balance we have U=X This result is secured when the relativevalues and signs of the impedances are properly chosen as shown by thefollowing formulae.

DM (21) m (23) X=NP+(M+N)E adding Equations '22 and 23, we get (24)X+U=NP+2(M+N)E substituting 19 in 24, we get (25) NP=-2MIE-2NE orcollecting terms (26) N(P+2E)=21\m substituting 21 in 26, we get (27)(P+2E)D=-2E(F+P) expanding, we get Now assuming that D, E and F are purereactances equal to ad, ie and if respectively, and that P is equal tor+7's, then I Equating imaginary and real components sep 'arately wederive two separate equations 30 and 31, as follows:

Now substituting -d for 2e in Equation 30, we obtain n Consequently thereactances F and D must be equal in magnitude and opposite in sign andreactance E must have one-half the value of reactance D and must equalin, sign reactance F. The two possibilities are illustrated in Figs. 3and 4.

In actual practice it has been found convenient to connect circuits ofthe type illustrated in Figs. 1, 2, 3 and 4 to the tank circuit of thelast amplifier stage in the transmitter in a. manner shown in Figs. '7,8, 9 and 10. The method shown in Fig. 7 when employed. in connectionwith the circuit shown in Fig. 1 possesses the advantage that bothconductors at the transmission line are connected directly to groundduring the operation of the circult so that any static charges which mayaccumulate on the antenna during rain or snow can leak off to groundwhereby high static potentials may be avoided without the use of anyauxiliary resistors or other means of grounding the transmission line.Moreover, the adjustments obtainable from this type of circuit aresuflicient to take care of a fairly wide range of line impedances sothat even when the transmission line is not flat, that is when it is notperfectly matched to the antenna, the tank circuit of the transmittermay still be properly loaded and the power transferred from the lastamplifier to the transmission line in an eiiicient way. It has aiso beenfound in practice that the circuit shown in Fig. 8 is particularly welladapted for use in conjunction with .the circuit shown in Fig. 2 for inthiscase the impedance which is usually obtained between terminals i and2 is capacitative so that part of the inductance it is alrea balancedout and condenser I may be fairly large and consequenty the adjustmentsare not very critical and it is found that the tank circuit may beloaded with reasonable ease without the use of unreasonable capacitiesand inductanees.

Either one of the circuits shown inF'igs. 3 and 4 may be employed. inconnection with the arrangements shown in Figs. 7 and. 8. The circuitshown in Fig. 9 may also be used. in conjunction with any one of thefour circuits shown in Figs. 1,

2, 3 and 4 when the impedance of the line is such thatthis circuit ismore advantageous. Fig. 9 illustrates the connection when the circuit ofFig.

i is employed, and Fig. it) illustrates the connection when the circuitof Fig. 3 is used. The network components used for obtaining balance arein the circuits of Figs. 7, 8, 9 and 10 isolated from the high directcurrent potentials used on the plate of the last tube, by a transformer,usually of the step-down type, and therefore these components andespecially the condensers may be 1 and 2 since the method employed inconnection with these circuits is applicable, with minor modiflcation,to the other circuits.

It is well known that at the higher frequencies the losses are to befound mainly in the inductive reactors, namely coils, while the lossesin condensers are comparatively low. Moreover, it is also quite wellknown that the losses in coils may be approximately determined from thesocalled constant Q whose value is given by the equation where L is theinductance of the coil w=1r frequency. v

The value of Q for ordinary transmitting coils is fairly well known andis usually somewhere around 150 or 200.

Upon the assumption that the Q factor and hence the resistance of thetwo coils of equal inductance, shown in Fig. 1, is the same the totalloss H in both coils may be expressed by theformula 0n the other hand Wthe power delivered tothe line is Now if we assume that, as is usuallythe case, the impedance P 01' the transmission line is a pure resistance(1. e. if we assume that zis=0 and r=P) and if we remember that A=C (asshow'nby Equation 17) then we may write Equation 5 as follows:

But since impedance A=R+ioL and since this impedance is very nearly apure reactance we may replace A by awL in Equation 37 thus givingSubstituting this in we obtain p as may be seen from the equation 41.

39 rem {5 32) Now substituting 36 and 34 in 39 we get WLw r V W 'Lw.(40) H= now let (41) v +Z )=K so that 40 may be written W tOA) K Hencethe loss H in the two coils depends upon the useful power W which in anygiven case is fixed, the factor Q of the coils which is made as large aspossible, and the coefficient K which depends upon Fig. 11 shows how theloss H in the two coils varies with the dimensions of the. two coils, orrather, with the value of L4 7 From this figure it may be seen that thesmallest value of K; that is the least losses for a given power, outputand a given Q factor, are obtained when 7 is equal to .707. The value ofK corresponding to such a value of V is 2.828. Therefore in this casezl'szsw Q From Fig. 11 itmay be seen that the minimum is not at allsharp but there is a whole region where the losses are reasonably low.In actual practice, it is generally possible to design the circuit insuch a manner that the circuit operates somewherewithin this minimumloss region. It is quite obvious from Fig. 11 that small coils and largecondensers are to be avoided in spite of the ers and reactances whichfall within usual rule which is very often followed, namely; that forminimum loss small coils and large condensers are to be preferred.Fig.-11' deflnitely shows that this rule does not apply to the circuitshown in Fig. 1.

A similar calculation in connection with the circuit illustrated in Fig.2 gives the following re- This result is illustrated in Fig. 12. Fromthis figure again it may be seen that there is a certain best value ofcondensers and inductances to be used in this second circuit for minimumloss but again the region is fairly wide and in practice it is fairlyeasy to choose values of condensthe minimum loss region. I

The smallest value of K1 corresponding to the least losses for a givenpower output W and a given coil factor Q occurs when -"=.z5 .I' Thevalue of K1 for this condition is 2.00. Itwill be noted that thisminimum value of K1 is about 29 per cent lower than the minimum value ofK for the circuit of Fig. 1.

It may be pointed out that a circuit employing two condensers and onereactor is somewhat more eflicient from thepoint of view of loss thancircuit l which employed two reactors and only one condenser. However,circuit 1 possessed other advantages. In practice, of course, the lossesin circuit l are quite low so that very often other advantages ofcircuit I may out-weigh the low loss property. of circuit 2. On theother hand, when the losses are the controlling feature and grounding isprovided for insome other manner, circuit 2 may be preferred. The samesort of considerations apply to circuits illustrated in Figs. 3 and 4.

' From the preceding description it will be seen that on the assumptionthat the impedances are pure reactances-the balance of the line will notbe affected by a change in the load. Furthermore even when the resistivecomponents of the inductance coils used are taken into account from thestandpoint of losses it will be noted that the power loss is not greatlyafiected by moderate changes in the load.

While I have described certain embodiments of my invention for thepurposes of illustrationit will be understood that various modificationsand adaptations thereof may be made within the spirit, of the inventionas set forth in the appended claims.

What I claim is:

1. An electrical network adapted to insure that currents traversingthetwo conductors of a two, wire transmission line are of substantiallyequal magnitude and opposite phase comprising three reactances, two ofwhich are of t e same sign and two wires, and the third between one of said two wires and ground, 7

2. A system in accordance with claim'l wherein the two reactances of thesame sign are of equal value and the impedance of the third reactance isequal in magnitude to one-half that of either of said two reactancesfirst mentioned.

3. An electrical network having two input terminals and two outputterminals and adapted to maintain voltages equal in magnitude andopposite in sign, between each of said output terminals and a given oneof said input terminals, comprising three reactances two of which are ofthe same sign and the third of which is of the opposite sign, the firstof said three reactances being connected in series between an inputterminal and an output terminal, a second of said reactances beingconnected between the same said input terminal and the other of saidoutput terminals and the third of said reactances being connectedbetween said other output terminal and the other of said inputterminals.

4. An electrical network according to claim 3 wherein said first andsaid second of said reactances are of equal magnitude and opposite signand said third reactance is of the same sign as said second reactanceand of one half its value.

5. An electrical network equal voltages between each of two outputterminals'and a given one of two input terminals comprising threereactances, a first and a second of the same sign and a third of theopposite sign, each having a first and a second terminal, all of saidfirst terminals being connected together, the second terminals of saidfirst and third reactances constituting said two input terminals and thesecond terminals of said first and second reactances constituting saidtwo output terminals.

6. An electrical network in accordance with claim 5 wherein said firstand second reactances are of the same sign and of equal magnitude andsaid third reactance is such that the impedance across it is equal inmagnitude to one-half of the impedance of either said first or saidsecond impedance and has an opposite sign.

7. In a radio system, radio translating apparatus including anamplifying tube, a two wire transmission line and means forinterconnecting said apparatus and said line. so as to. minimize energytransfer between said line and the surrounding space, comprising anetwork of three reactances, two of which are of the same sign and thethird or which is of the opposite sign, one of said three reactancesbeing connected in series in one of said two wires, another in shunt tosaid two wires, and the third between one of said two wires and ground,a tuned circuit coupled to the output circuit of said amplifying tube;and means connecting said tuned circuit across two of the reactances ofsaid network.

8. In a radio system, radio translating apparatus including anamplifying tube, a two wire transmission line connected thereto, meansfor interconnecting said apparatus and said line so as to minimizeenergy transfer between said line and the surrounding space, comprisinga network of three reactances, two of which are of the same sign and thethird of which is of the opposite sign, one of said three reactancesbeing connected in series in one of said two wires, another in shunt tosaid two wires, and the third between one of said two wires and ground,a first tuned circuit connected in the plate circuit of said amplifyingtube, a second tuned circuit magnetically coupled to said first tunedcircuit, means connecting said second tuned circuit across two of thereactances adapted to maintain of said network, and means connecting toground a point in said second tuned circuit.

9. An electrical network adapted to insure that currentstraversing thetwo conductors of a two wire transmission line are of substantiallyequal magnitude and opposite phase comprising three reactances, areactance of one sign being connected in series in one of said twowires, a reactance of the same sign being connected in shunt to said twowires and a reactance of the opposite sign being connected between saidtwo wires and ground.

10. An electrical network adapted to insure that currents traversing thetwo conductors of a two wire transmission line are of substantiallyequal magnitude and opposite phase comprising three reactances, two ofwhich are of the same sign and the third of which is of the oppositesign, a reactance of one sign being connected in series in one of saidtwo wires, a reactance of the 0p- ,posite sign being connected in shuntto said two wires and a third reactance having the same sign as saidreactance of one sign connected between one of said two-wires andground.

11. An electrical network adapted to insure that currents traversing thetwo conductors of a two wire transmission line' are of substantiallyequal magnitude and opposite phase'comprising three reactances, two ofwhich are inductive and equal in magnitude and thethird of which iscapacitative and has a magnitude equal to onehalf that of either of saidinductive reactances, one of the inductive reactances being connected inseries in one of said two wires, the capacitative reactance beingconnected in-shunt to said two wires and the other inductive resistancebeing connected between one of said two wires and ground, the impedancein ohms of each of said inductive reactances being equal to 2.828 timesthe resistance of said line together with said antenna.

12. An electrical network adapted to insure that currents traversing thetwo conductors of a two wire transmission line are of substantiallyequal magnitude and opposite phase comprising three reactances, two ofwhich are capacitative and equal in magnitude and the third of which isinductive and has a magnitude equal to one-half that of either of saidcapacitative reactances, one of the capacitative reactances beingconnected in series in one of said two wires, the inductive reactancebeing connected in shunt to said two wires and the capacitativereactance being connected between one of said two wires and ground, theimpedance in ohms of said inductive reactance being equal to 2.00 timesthe resistance of said line together with said antenna.

13. An electrical network having a first pair of terminals and a secondpair of terminals and adapted to maintain voltages equal in magnitudeand opposite in sign between each terminal of said first pair and agiven terminal of said second pair, comprising three reactances two ofwhich second pair, and the third of said reactances being connectedbetween said other terminal of said second pair and the other terminalof said first pair.

ANDREW ALFORD.

